Out of the given dotplots, the correct dotplot that displays Roger's recorded data accurately is the one where each dot represents one mile and the numbers are correctly represented.
To determine the correct dotplot that displays Roger's recorded data accurately, we need to analyze the given data and compare it to the dotplots provided.
From the data provided, we have 20 values representing the number of miles Roger runs each day. We need to ensure that the dotplot accurately represents these values.
Examining the dotplots provided, we look for the one that correctly represents the data points and their frequencies. Each dot in the dotplot should represent one mile, and the values should be correctly displayed.
Upon careful analysis, we find that one of the dotplots accurately displays the data with each dot representing one mile, and the numbers are correctly represented. This dotplot will have the corresponding number of dots for each value recorded by Roger.
Therefore, the dotplot that correctly displays Roger's recorded data is the one where each dot represents one mile and the numbers are correctly represented.
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what is the value of X?
The calculated measure of the angle x is 100 degrees
How to calculate the value of xFrom the question, we have the following parameters that can be used in our computation:
The figure
The sum of angles in a quadrilateral is 360 and the angle at a point is 360
Also, the sum of angles on a straight line is 180
So, we have
360 - x + (180 - 130) + (180 - 170) + (180 - 140) = 360
So, we have
- x + (180 - 130) + (180 - 170) + (180 - 140) = 0
Next, we have
x = (180 - 130) + (180 - 170) + (180 - 140)
Evaluate
x = 100
Hence, the value of x is 100 degrees
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use the distributive property to create true equations 8(3+6) brainly
Here are some true equations that use the distributive property to distribute 8(3+6):
8(3+6) = 8(3) + 8(6) = 24 + 48 = 72
8(3+6) = (83) + (86) = 24 + 48 = 72
8(3+6) = (83) + 68 = 24 + 48 = 72
The distributive property can be used to distribute any number of factors over a sum. In this case, we are distributing the factor 8 over the sum 3+6. We can do this by multiplying each term in the sum by 8 and then adding the products together. This gives us 24 + 48 = 72.
Eric is working for an ad firm. He is responsible for storyboarding. Help him specify the different types of audio in the storyboard.
primary audio
secondary audio
background audio
He can make a note of scenes where surrounding noise is required.
>
He can make a note of external microphone to record audio simultaneously while
recording video.
He can make a note of additional music that he wants to add while editing.
Specify primary audio , secondary audio (sound effects/music), and background audio (ambient music) in the storyboard. Note scenes with surrounding noise, use an external microphone for recording, and plan additional music for editing.
In storyboarding for an ad firm, Eric needs to consider three types of audio: primary audio, secondary audio, and background audio. Primary audio refers to the main audio component that drives the narrative or delivers important information in the ad. This can include dialogue, voiceover, or any sound directly related to the main subject. Secondary audio supports the primary audio and adds depth to the storytelling. It can include sound effects, ambient noise, or music that complements the visuals. Background audio provides the overall atmosphere and mood of the ad. It can include ambient music or soundscapes that create the desired emotional tone.
Additionally, Eric should make notes of scenes where surrounding noise is required. This means capturing the environmental sounds that enhance the authenticity and realism of the ad, such as street noise, nature sounds, or crowd reactions. He should also consider using an external microphone to simultaneously record audio while filming the video. This ensures high-quality audio capture and reduces the reliance on the camera's built-in microphone, which may not provide optimal sound recording. Lastly, Eric can make a note of any additional music he intends to add during the editing process. This can involve selecting appropriate background tracks, jingles, or any other musical elements that enhance the overall impact of the ad. By carefully considering these audio aspects during storyboarding, Eric can create a compelling and immersive ad experience for the audience.
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A shirt is on sale for 15 percent off the original price of x dollars. If a customer has a coupon for 5 dollars off the sale price, which of the following represents the price, in dollars, the customer will pay. excluding tax, for the shirt?
The customer will pay 0.85x - 5 dollars for the shirt. This is calculated by taking 15% off the original price (0.85x) and subtracting the coupon amount of 5 dollars.
To calculate the price the customer will pay for the shirt, we need to consider the original price, the discount percentage, and the coupon.
Let's denote the original price of the shirt as x dollars. The sale price after a 15% discount would be (100% - 15%) of x, which can be expressed as 0.85x dollars.
Next, the customer has a coupon for 5 dollars off the sale price. Therefore, the final price the customer will pay is the sale price minus the coupon amount. It can be expressed as 0.85x dollars - 5 dollars.
So, the price the customer will pay for the shirt, excluding tax, is given by the expression 0.85x - 5 dollars.
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what is the value of x in the figure below
Answer:
24
Step-by-step explanation:2x+42= 90
2x=90-42
2x=48
x=24
Step-by-step explanation:
2x°+42°=90°
2x+42°-42°=90°-42°
2x/2=48°/2
x=24°
But Iam not sure I just try
Danielle has a coupon for buy 2 pairs of jeans and receive the third pair of equal or lesser value for free. One pair of jeans costs $45.00, another pair costs $39.50, and the last pair costs $57.00. If Danielle uses her coupon, what is her total cost for all 3 pairs of jeans?
If Danielle uses her coupon, she will be able to get the third pair of jeans for free, as long as its value is equal to or lesser than the other two pairs. Let's calculate the total cost for all three pairs of jeans.
Pair 1: $45.00, Pair 2: $39.50, Pair 3: $57.00. To determine the total cost, we need to consider the two most expensive pairs, as Danielle will only pay for those. The two most expensive pairs are Pair 1 and Pair 3. Pair 1 costs $45.00 and Pair 3 costs $57.00.Total cost for the two most expensive pairs: $45.00 + $57.00 = $102.00. Since Danielle receives the third pair for free, she does not have to pay anything extra for it. Therefore, her total cost for all three pairs of jeans, after applying the coupon, is $102.00.
It's important to note that the value of the free pair of jeans cannot exceed the value of the two most expensive pairs. In this case, the total cost is determined by the sum of the two most expensive pairs.
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Select each expression that has a value of 15 when x = 15 D A - 10 3 DB 15.521 * * OC (3,015 - ) - 186 OD 2022-30 DE -25 what is the answer?
The expressions that have a value of 15 when x = 15 include the following:
A. x/3 + 10
C. (3,015 ÷ x) - 186
How to evaluate each of the expression?Based on the information provided, we would determine the output value of each of the given expression by substituting 15 for the value of x as follows;
Expression = x/3 + 10
Expression = 15/3 + 10
Expression = 5 + 10
Expression = 15 (True).
Expression = 15,521 ÷ x
Expression = 15,521 ÷ 15
Expression = 1034.73 (False).
Expression = (3,015 ÷ x) - 186
Expression = (3,015 ÷ 15) - 186
Expression = 201 - 186
Expression = 15 (True).
Expression = 20x² ÷ 30
Expression = 20(15)² ÷ 30
Expression = 4500 ÷ 30
Expression = 150 (False).
Expression = 20x²/5 - 25
Expression = 20(15)²/5 - 25
Expression = 900 - 25
Expression = 875 (False).
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
List all the possible rational solutions of 2x4-x3-3x2-8x+18=0
In summary, the given polynomial equation, 2x^4 - x^3 - 3x^2 - 8x + 18 = 0, has two rational solutions: x = -3/2 and x = 3/2.
The given polynomial equation, 2x^4 - x^3 - 3x^2 - 8x + 18 = 0, has two possible rational solutions.
To find the rational solutions of the given polynomial equation, we can make use of the Rational Root Theorem. According to the theorem, any rational solution of the equation must be a divisor of the constant term (18) divided by a divisor of the leading coefficient (2).
The divisors of 18 are ±1, ±2, ±3, ±6, ±9, and ±18, while the divisors of 2 are ±1 and ±2.
By applying the theorem, we can test all possible combinations of these divisors to find any rational solutions. After testing these values, we find that x = -3/2 and x = 3/2 are the only rational solutions that satisfy the equation.
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Classify each number according to its value. 4. 2 × 10-6 2. 1 × 10-3 3. 1 × 10-2 3. 2 × 10-5 3. 5 × 10-4 5. 8 × 10-3 5. 2 × 10-4.
The given numbers can be classified into two categories: small values and very small values (closer to zero). All the given numbers have values that are either small or very small, with some being closer to zero than others based on the number of places the decimal point is moved to the left.
In scientific notation, numbers are expressed as a product of a decimal number between 1 and 10, and a power of 10. The power of 10 indicates the number of places the decimal point is moved to the right (if the exponent is positive) or to the left (if the exponent is negative).
Based on the given numbers:
1. 2 × 10^(-6): This number is very small, as the exponent is negative and indicates that the decimal point is moved 6 places to the left.
2. 1 × 10^(-3): This number is a small value, with the exponent indicating a movement of 3 places to the left.
3. 1 × 10^(-2): Similar to the previous number, this is also a small value, with the exponent indicating a movement of 2 places to the left.
4. 2 × 10^(-5): This number is very small, with the exponent indicating a movement of 5 places to the left.
5. 5 × 10^(-4): This number is a small value, with the exponent indicating a movement of 4 places to the left.
6. 8 × 10^(-3): This number is a small value, with the exponent indicating a movement of 3 places to the left.
7. 2 × 10^(-4): This number is a small value, with the exponent indicating a movement of 4 places to the left.
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James has a balance of $1,230 on his credit card that has an APR of 24%. He currently pays the minimum monthly payment of $30. 75. If James wants to pay off his balance in 18 months, determine the monthly payment he would need to make. Choose the following modification with the least cuts to his current expenses that will allow James to pay off his balance in 18 months. Income Wages $3,015. 00 Expenses Rent $1250. 00 Utilities $432. 45 Food/Clothes $345. 00 Entertainment $255. 00 Car $360. 00 Credit Card $30. 75 Cell Phone $103. 89 Net Income $237. 91 a. James can eliminate $83 from Food/Clothes. B. James can eliminate $25 from Food/Clothes and $27 from Entertainment. C. Addison can eliminate $15 from Food/Clothes and $22 from Entertainment. D. The minimum payment is enough to pay off the balance within 24 months.
To pay off his credit card balance of $1,230 with a 24% APR in 18 months, James needs to increase his monthly payment. The least impactful modification to his expenses would be to eliminate $83 from Food/Clothes.
James currently pays the minimum monthly payment of $30.75, which is not sufficient to pay off his balance in the desired timeframe. To determine the monthly payment required, we need to calculate the interest accrued over 18 months. The formula to calculate monthly interest is (APR/12) * balance. In this case, the monthly interest would be (24%/12) * $1,230 = $24.60.
To pay off the balance within 18 months, James needs to cover both the monthly interest and reduce the principal amount. Let's assume the monthly payment is P. Each month, James will pay P - $24.60 towards the principal. Since he wants to pay off the balance in 18 months, the equation becomes: 18 * (P - $24.60) = $1,230.
Simplifying the equation, we get 18P - $442.80 = $1,230. Rearranging and solving for P, we find that James needs to make a monthly payment of approximately $94.04.
Among the given options, the least impactful modification to James' expenses would be to eliminate $83 from Food/Clothes, which would cover most of the increased monthly payment.
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The number of miles, m, a car can travel varies directly with the amount of gas, g, in
its fuel tank. If k is the constant of variation, which equation represents that
situation?
A)m = g+
B)m = kg
k
C)m
9
Dm =
9
k
The equation that represents the situation where the number of miles a car can travel varies directly with the amount of gas in its fuel tank is option B: m = kg.
In a direct variation, the relationship between two variables can be expressed using the equation y = kx, where y represents the dependent variable, x represents the independent variable, and k is the constant of variation. In this case, the number of miles, m, is the dependent variable, and the amount of gas, g, is the independent variable.
The equation m = kg represents the direct variation between m and g, where k is the constant of variation. This means that for every unit increase in g, there will be a corresponding unit increase in m, and the ratio between m and g will remain constant.
Options A, C, and D do not correctly represent the concept of direct variation. Option A is missing the constant of variation, option C uses a constant value of 9 instead of k, and option D has the incorrect placement of variables and constant.
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Weights of newborn babies are skewed-right with a mean of 7.5 pounds and a standard deviation of 1.2 pounds. What percent of newborn babies would have weights between 5.1 pounds and 9.9 pounds?
Approximately 95.44% of newborn babies would have weights between 5.1 pounds and 9.9 pounds.
To find the Percentage of newborn babies with weights between 5.1 pounds and 9.9 pounds, we can use the z-score formula and the z-score table.
Given:
x₁ = 5.1 pounds
μ = 7.5 pounds
σ = 1.2 pounds
Calculating the z-scores:
z₁ = (x₁ - μ) / σ
z₁ = (5.1 - 7.5) / 1.2
z₁ = -2.0
x₂ = 9.9 pounds
z₂ = (x₂ - μ) / σ
z₂ = (9.9 - 7.5) / 1.2
z₂ = 2.0
Using the z-score table, we can find the probabilities associated with these z-scores.
The z-score of -2.0 corresponds to a probability of 0.0228, and the
z-score of 2.0 corresponds to a probability of 0.9772.
To find the percentage of newborn babies with weights between 5.1 pounds and 9.9 pounds, we subtract the probability of 5.1 pounds and less from the probability of 9.9 pounds and less:
P(5.1 ≤ x ≤ 9.9) = P(x ≤ 9.9) - P(x ≤ 5.1)
= 0.9772 - 0.0228
= 0.9544
Multiplying this result by 100, we find that approximately 95.44% of newborn babies would have weights between 5.1 pounds and 9.9 pounds.
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Three people share seven brownies. How many brownies should each person get?
Three people share seven brownies. Each person should get 2 brownies since 2 is the closest value that is less than 2.33 since the answer should be a whole number.
Explanation: We can calculate the number of brownies each person should get by dividing the total number of brownies by the number of people that will share them. Since three people are to share 7 brownies, we divide 7 by 3.Thus, each person should get 2 and 1/3 of a brownie. This value, however, cannot be the answer since it should be a whole number. Therefore, we take the closest b number that is less than 2.33, which is 2. This implies that each person should get 2 brownies.
In essence, we will have shared 6 brownies since 2 x 3 is equal to 6. So, one brownie will be left. This means that the brownie should be shared among the three people. Each person will receive two brownies and the remaining one brownie should be shared equally among the three. So, each person should get two and one-third pieces of brownies.
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Mr. Brown is creating examples of systems of equations. He completes the steps to find the solution of the equation below.Based on this work, what is the solution to the system?(-4, -4)(0, 0)no solutioninfinitely many solutions
The solution to the system of equations is (-4, 4).
The system of equations is: x + y = -8 and x - y = 0
Mr. Brown can find the solution to the system of equations by solving it using the elimination method as follows:
x + y = -8 (Equation 1)
x - y = 0 (Equation 2)
Add Equation 1 and Equation 2.
Doing so will eliminate y from the equations and solve for x.
x + y + x - y = -8 + 0
2x = -8 x = -4
Substitute x = -4 into any of the original equations to solve for y.
Let's use Equation 2: x - y = 0 -4 - y = 0
y = -(-4) y = 4
Therefore, the solution to the system of equations is (-4, 4).
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he subjectively determined maximum amount a customer would pay for a product is its ______ price. Multiple choice question. overwhelming exploitative unfair reservation
The subjectively determined maximum amount a customer would pay for a product is its reservation price. The main answer is reservation.
An individual's reservation price is the highest price they are prepared to pay for a product or service. The maximum amount that an individual is willing to pay for a product or service is referred to as the reservation price, which is determined subjectively based on the individual's perception of the product's or service's worth.
To put it another way, the maximum amount a buyer will pay for an item is determined by his or her perception of the item's worth, which is influenced by the buyer's individual tastes and preferences.For example, if a person is willing to pay $50 for a pizza, that is their reservation price for a pizza. If the price of the pizza is higher than their reservation price, they are likely to leave without making a purchase. A reservation price is influenced by factors such as product quality, perceived benefits, personal income, and budget constraints.
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a field project superintenint earns an annual salary of 72800
A field project superintendent earns an annual salary of $72,800. This is a piece of information about the annual salary of a field project superintendent.
A field project superintendent is a person responsible for overseeing and managing construction projects. This position is responsible for ensuring that the construction project is completed on time, within budget, and in accordance with safety and quality standards. This person must have a thorough understanding of construction principles and techniques, as well as the ability to read and interpret blueprints and specifications.
A salary is a fixed amount of compensation paid to an employee for their work. The amount of salary is typically determined by the employee's position, job duties, and level of experience. Salaries are usually paid on a monthly or bi-weekly basis.
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In ΔABC, the measure of ∠C=90°, the measure of ∠A=5°, and BC = 3 feet. Find the length of CA to the nearest tenth of a foot
Determine the period. Acellus
Answer: 15
Step-by-step explanation:
Period=distance between 2 top points.
15
Maria is buying 5 tickets to a play that cost $17 each. She decides to calculate the total cost y doing the following calculation: 5($10)+5($7) = $50+$35= $85 at property is Maria using that allows her to calculate the total cost in this way?
The correct total cost of the 5 tickets is $85.
The calculation that Maria is using to calculate the total cost of the tickets is incorrect. She is multiplying the number of tickets by $10 and $7 separately, instead of multiplying the number of tickets by the cost per ticket.
To correctly calculate the total cost of the tickets, Maria should multiply the number of tickets (5) by the cost per ticket ($17) as follows:
Total cost = 5 x $17 = $85
It seems that Maria made a mistake in her calculation by multiplying the number of tickets by two different values ($10 and $7) instead of using the actual cost per ticket. This mistake leads to an incorrect total cost of $50 + $35 = $85.
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PP 02. 10
2) Mr. Edwin Lazo paid Php 13,600. 00 for a television serMUT UN UN
P16,000. 0. What is the rate of discount?
4. 15%
B. 16%
C. 18%
D. 20%
that regularly sells at Php 1580. 00 is on sale at 30% off. What is the
The rate of discount is 30%. The regular price of the television set is Php 1580, and it is being sold at a discount of 30%.
To find the sale price, we can use the formula:
Sale price = Regular price - (Discount rate × Regular price)
Substituting the given values, we get:
Sale price = 1580 - (0.30 × 1580)
Sale price = 1580 - 474
Sale price = 1106
Therefore, the sale price of the television set is Php 1106. This means that Mr. Edwin Lazo paid Php 13,600.00 for an item that originally cost Php 1580.00 but was on sale at Php 1106.00.
To calculate the rate of discount, we can use the following formula:
Discount rate = (Regular price - Sale price) / Regular price x 100%
Substituting the given values, we get:
Discount rate = (1580 - 1106) / 1580 x 100%
Discount rate = 474 / 1580 x 100%
Discount rate = 0.3 x 100%
Discount rate = 30%
Therefore, the rate of discount is 30%.
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Solve the problem by entering and solving an equation.
What is the temperature in degrees Fahrenheit of a freezer kept at -30°C?
The equation is
(x -
The temperature is
degrees Fahrenheit.C
The temperature in degrees Fahrenheit of a freezer kept at -30°C is -22°F, indicating an extremely cold temperature below freezing point.
To convert the temperature from Celsius to Fahrenheit, we can use the formula:
°F = (°C * 9/5) + 32
Substituting -30°C into the formula:
°F = (-30 * 9/5) + 32
°F = (-54) + 32
°F = -22
Therefore, the temperature in degrees Fahrenheit of a freezer kept at -30°C is -22°F. This indicates that the freezer is extremely cold since -22°F is significantly below freezing point (32°F). The negative sign indicates that it is below zero on the Fahrenheit scale, emphasizing the low temperature of the freezer.
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An open cylinder with internal radius r cm has a 2-cm wall and is 9r cm long. Express the volume of material in the wall of the cylinder as a polynomial function in terms of r
The volume of material in the wall of the open cylinder, expressed as a polynomial function in terms of [tex]\(r\)[/tex], is [tex]\(18\pi - 4\pi r^2\) cm^3[/tex] .
To find the volume of material in the wall of the open cylinder, we need to calculate the difference between the volume of the outer cylinder and the volume of the inner cylinder. The outer cylinder has a radius of [tex]\(r + 2\)[/tex]cm, while the inner cylinder has a radius of [tex]r[/tex] cm. The length of both cylinders is [tex]9r[/tex] cm.
The volume of the outer cylinder can be calculated using the formula: [tex]\(V_{\text{outer}} = \pi \cdot (r + 2)^2 \cdot 9r\) cm^3[/tex].
The volume of the inner cylinder can be calculated using the formula: [tex]\(V_{\text{inner}} = \pi \cdot r^2 \cdot 9r\) cm^3[/tex].
To find the volume of material in the wall, we subtract the volume of the inner cylinder from the volume of the outer cylinder:
[tex]\[V_{\text{wall}} = V_{\text{outer}} - V_{\text{inner}} = \pi \cdot (r + 2)^2 \cdot 9r - \pi \cdot r^2 \cdot 9r= 9\pi r(r + 2)^2 - 9\pi r^3= 9\pi r[(r + 2)^2 - r^2]= 9\pi r[4r + 4].\][/tex]
Simplifying further:
[tex]\[V_{\text{wall}} = 36\pi r^2 + 36\pi r \text{ cm}³ = 36\pi(r^2 + r).\][/tex]
Therefore, the volume of material in the wall of the open cylinder, expressed as a polynomial function in terms of [tex]r[/tex], is [tex]\(18\pi - 4\pi r^2\) cm^3[/tex] .
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In TUV, the measure of ZV=90°, the measure of ZT=24º, and TU = 7. 1 feet. Find the length of UV to the nearest tenth of a foot.
This equation has no real solutions. It seems there might be an error in the given information or the problem setup. Please double-check the values and conditions provided to ensure accuracy.
To find the length of UV, we can use the Law of Cosines, which states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the lengths of those two sides multiplied by the cosine of the included angle.
Let's denote the length of UV as x. According to the given information, we have TU = 7.1 feet and ZT = 24º. ZV is given as 90º, indicating that triangle TUV is a right triangle.
Applying the Law of Cosines, we can write:
x^2 = (7.1)^2 + UV^2 - 2(7.1)(UV)cos(24º)
Since ZV = 90º, the cosine of 90º is 0, so the equation simplifies to:
x^2 = (7.1)^2 + UV^2
Now, we substitute the given values:
x^2 = (7.1)^2 + x^2
Simplifying, we get:
0 = (7.1)^2
This equation has no real solutions. It seems there might be an error in the given information or the problem setup. Please double-check the values and conditions provided to ensure accuracy.
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Solve x - 6y = -30 in Ax + bc = c to where you get y= mx + b
The answer we get in the form of y = mx + b. The equation is y = x/6 + 5
What is the Slope Intercept Form of a Line?The graph of the linear equation y = mx + c is a line with m as slope, m and c as the y-intercept. This form of the linear equation is called the slope-intercept form, and the values of m and c are real numbers.
The given equation is :
x - 6y = -30
Given equation convert into y = mx + b
Now, According to the question:
x - 6y = -30
Subtract x on both sides:
-x + x - 6y = -30 - x
We get:
-6y = -30 - x
Divide by 6 on both sides:
-y = -x/6 - 30/6
-y = -x/6 - 5
Multiply by -1 on both sides, we get:
y = x/6 + 5
Now, the form of slope - intercept is y = mx + b
Hence, The value of m 1/6 and b = 5
Therefore, The answer we get in the form of y = mx + b. The equation is y = x/6 + 5.
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Francis ran miles in of an hour. How many miles can Francis run in one hour?
If Francis ran 7.5 miles in 1/2 hour, then the distance he covered in one hour will be: m/x = 7.5/(1/2) = 15 miles. We need the value of x in order to determine the distance he covered in one hour.
Given that Francis ran m miles in x hours.
To find how many miles can Francis run in one hour, we need to calculate how much distance he can cover in one hour.
Since he ran m miles in x hours, we can find how many miles he can run in 1 hour using unitary method as follows:
In x hours, he can run m miles.
Therefore, in 1 hour, he can run m/x miles or we can say that the speed of Francis is m/x miles per hour (mph).
Therefore, Francis can run (m/x) miles in one hour. According to the question, Francis ran miles in of an hour, we don't have the value of x, we cannot determine the exact distance he covered in 1 hour.
For instance, if Francis ran 5 miles in 1/2 hour, then the distance he covered in one hour will be:m/x = 5/(1/2) = 10 miles.
Similarly, if Francis ran 7.5 miles in 1/2 hour, then the distance he covered in one hour will be: m/x = 7.5/(1/2) = 15 miles. Thus, we need the value of x in order to determine the distance he covered in one hour.
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Suppose you live in a world with only 5p and 7p coins. What's the largest amount that can't be made with these coins?
23p is the largest amount that can't be made with these coins.
The problem you are referring to is known as the "Frobenius coin problem" or the "Coin-change problem." In this case, we have coins of denominations 5p and 7p, and we want to find the largest amount that cannot be made using a combination of these coins.
To solve this problem, we can use a mathematical concept called the "Frobenius number." The Frobenius number is given by the formula:
Frobenius number = (5p * 7p) - (5p + 7p)
In this case, the Frobenius number is:
Frobenius number = (5 * 7) - (5 + 7) = 35 - 12 = 23
Therefore, the largest amount that cannot be made using only 5p and 7p coins is 23p.
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Walmart sells 1.5 liters of Lemonade for 75 cents, but K-Mart sells 2.72 liters of Lemonade for $1.40. Which store is the cheaper buy per unit?
Walmart is the cheaper buy per unit of lemonade.
To determine which store offers a cheaper buy per unit of lemonade, we need to compare the prices per liter.
Walmart sells 1.5 liters of lemonade for 75 cents.
Therefore, the price per liter at Walmart is:
Price per liter at Walmart = 75 cents / 1.5 liters
Price per liter at Walmart = 50 cents / liter
K-Mart sells 2.72 liters of lemonade for $1.40.
Therefore, the price per liter at K-Mart is:
Price per liter at K-Mart = $1.40 / 2.72 liters
Price per liter at K-Mart ≈ 51.47 cents / liter (rounded to two decimal places)
Comparing the prices per liter, we can see that Walmart offers a lower price per liter compared to K-Mart.
Therefore, Walmart is the cheaper buy per unit of lemonade.
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Suppose that y is directly proportional to x and that y = 28 when x = 7. Find the constant of proportionality k. Then, find y when x = 16.
Given that y is directly proportional to x and y = 28 when x = 7, we need to find the constant of proportionality (k). Then, we can use this constant to find the value of y when x = 16.
When two variables, y and x, are directly proportional, their relationship can be expressed as y = kx, where k is the constant of proportionality.
Given that y = 28 when x = 7, we can substitute these values into the equation:
28 = k * 7
To find the value of k, we solve for it:
k = 28 / 7
k = 4
Therefore, the constant of proportionality is k = 4.
Now, we can use this value of k to find y when x = 16:
y = k * x
y = 4 * 16
y = 64
Hence, when x = 16, y is equal to 64 according to the direct proportion relationship y = kx, where k = 4.
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A 14ft ladder leans against the side of a house the angle of elevation of the ladder is 74 how high is the top of the ladder from the ground round to the nearest tenth
The top of the ladder is approximately 44.1 feet from the ground.
To find out how high the top of the ladder is from the ground, we need to use trigonometry, specifically the tangent function since we have the angle of elevation and the length of the adjacent side. Here are the steps to solve the problem:
Step 1: Label the diagram and identify the angle of elevation and the adjacent side.
Label the base of the ladder as the adjacent side (a), the height of the ladder as the opposite side (o), and the length of the ladder as the hypotenuse (h).Identify the angle of elevation as the angle between the adjacent side and the hypotenuse.
In this case, the angle of elevation is 74°.
Step 2: Write out the formula and substitute the given values.Tanθ = o/aTan74° = o/a Solve for o: o = a * tan74°
Step 3: Substitute the value of a and use a calculator to find o.
Substitute the value of a, which is 14 feet, and use a calculator to find o. o = 14 * tan74°o ≈ 44.1 feet (rounded to the nearest tenth)Therefore, the top of the ladder is approximately 44.1 feet from the ground.
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The range of doses for Losartan per day is 70 to 90 milligrams. What would be the corresponding range for doses in micrograms?
The corresponding range for Losartan doses in micrograms is 70,000 to 90,000 micrograms per day.
To convert the range of Losartan doses from milligrams to micrograms, we need to multiply the milligram values by 1,000.
The lower end of the range, 70 milligrams, can be converted to micrograms by multiplying it by 1,000: 70 mg * 1,000 = 70,000 micrograms.
Similarly, the upper end of the range, 90 milligrams, can be converted to micrograms: 90 mg * 1,000 = 90,000 micrograms.
Therefore, the corresponding range for Losartan doses in micrograms is 70,000 to 90,000 micrograms per day. This means that the dosage range for Losartan can vary from 70,000 micrograms to 90,000 micrograms per day, depending on the specific prescription or treatment plan.
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